Extending local gauge tansformations in a suitable way to Faddeev-Popov ghost fields, one obtains a symmetry of the total action, i.e., the Yang-Mills action plus a gauge fixing term (in a lambda-gauge) plus the ghost action. The anomalous Master Ward Identity (for this action and this extended, local gauge transformation) states that the pertinent Noether current -- the interacting ``gauge current'' -- is conserved up to anomalies. It is proved that, apart from terms being easily removable (by finite renormalization), all possible anomalies are excluded by the consistency condition for the anomaly of the Master Ward Identity, recently derived in refenrence [8].
{"title":"The power of the anomaly consistency condition for the Master Ward Identity: Conservation of the non-Abelian gauge current","authors":"Michael Duetsch","doi":"arxiv-2409.10122","DOIUrl":"https://doi.org/arxiv-2409.10122","url":null,"abstract":"Extending local gauge tansformations in a suitable way to Faddeev-Popov ghost\u0000fields, one obtains a symmetry of the total action, i.e., the Yang-Mills action\u0000plus a gauge fixing term (in a lambda-gauge) plus the ghost action. The\u0000anomalous Master Ward Identity (for this action and this extended, local gauge\u0000transformation) states that the pertinent Noether current -- the interacting\u0000``gauge current'' -- is conserved up to anomalies. It is proved that, apart from terms being easily removable (by finite\u0000renormalization), all possible anomalies are excluded by the consistency\u0000condition for the anomaly of the Master Ward Identity, recently derived in\u0000refenrence [8].","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the asymmetric simple exclusion process with non-diagonal boundary terms under a specific constraint. A symmetric chiral basis is constructed and a special string solution of the Bethe ansatz equations corresponding to the steady state is presented. Using the coordinate Bethe ansatz method, we derive a concise expression for the steady state. The current and density profile in the steady state are also studied.
{"title":"Bethe ansatz approach for the steady state of the asymmetric simple exclusion process with open boundaries","authors":"Xin Zhang, Fa-Kai Wen","doi":"arxiv-2409.09618","DOIUrl":"https://doi.org/arxiv-2409.09618","url":null,"abstract":"We study the asymmetric simple exclusion process with non-diagonal boundary\u0000terms under a specific constraint. A symmetric chiral basis is constructed and\u0000a special string solution of the Bethe ansatz equations corresponding to the\u0000steady state is presented. Using the coordinate Bethe ansatz method, we derive\u0000a concise expression for the steady state. The current and density profile in\u0000the steady state are also studied.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems. Potentials of this type are given by a superposition of periodic potentials and represent quasiperiodic functions on a plane with four quasiperiods. Here we study an important special case when the periodic potentials have the same rotational symmetry. In the generic case, their superpositions have ``chaotic'' open level lines, which brings them close to random potentials. At the same time, the Novikov problem has interesting features also for ``magic'' rotation angles, which lead to the emergence of periodic superpositions.
{"title":"On the Novikov problem for superposition of periodic potentials","authors":"A. Ya. Maltsev","doi":"arxiv-2409.09759","DOIUrl":"https://doi.org/arxiv-2409.09759","url":null,"abstract":"We consider the Novikov problem, namely, the problem of describing the level\u0000lines of quasiperiodic functions on the plane, for a special class of\u0000potentials that have important applications in the physics of two-dimensional\u0000systems. Potentials of this type are given by a superposition of periodic\u0000potentials and represent quasiperiodic functions on a plane with four\u0000quasiperiods. Here we study an important special case when the periodic\u0000potentials have the same rotational symmetry. In the generic case, their\u0000superpositions have ``chaotic'' open level lines, which brings them close to\u0000random potentials. At the same time, the Novikov problem has interesting\u0000features also for ``magic'' rotation angles, which lead to the emergence of\u0000periodic superpositions.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that the critical finite-size gap scaling for frustration-free Hamiltonians is of inverse-square type. The novelty of this note is that the result is proved on general graphs and for general finite-range interactions. Therefore, the inverse-square critical gap scaling is a robust, universal property of finite-range frustration-free Hamiltonians. This places further limits on their ability to produce conformal field theories in the continuum limit. Our proof refines the divide-and-conquer strategy of Kastoryano and the second author through the refined Detectability Lemma of Gosset--Huang.
我们证明了无挫折哈密顿的临界有限大小间隙缩放是反平方类型的。因此，反平方临界间隙缩放是有限范围无挫折哈密顿的一个稳健而普遍的特性。这进一步限制了它们在连续极限中产生共形场论的能力。我们的证明完善了卡斯托里亚诺和第二作者的分而治之策略，即通过高塞特--黄的精炼可探测性训令（Detectability Lemma of Gosset--Huang）。
{"title":"On the critical finite-size gap scaling for frustration-free Hamiltonians","authors":"Marius Lemm, Angelo Lucia","doi":"arxiv-2409.09685","DOIUrl":"https://doi.org/arxiv-2409.09685","url":null,"abstract":"We prove that the critical finite-size gap scaling for frustration-free\u0000Hamiltonians is of inverse-square type. The novelty of this note is that the\u0000result is proved on general graphs and for general finite-range interactions.\u0000Therefore, the inverse-square critical gap scaling is a robust, universal\u0000property of finite-range frustration-free Hamiltonians. This places further\u0000limits on their ability to produce conformal field theories in the continuum\u0000limit. Our proof refines the divide-and-conquer strategy of Kastoryano and the\u0000second author through the refined Detectability Lemma of Gosset--Huang.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on sphere and pseudosphere. Here we concentrate on Kepler-Coulomb potential models. We have used formulated in [6] the two-dimensional situation on the quantum level. The Sommerfeld polynomial method is used to perform the quantization of such problems. The quantization of two-dimensional problems may have something to do with the dynamics of graphens, fullerens and nanotubes. This problem is also nearly related to the so-called restricted problems of rigid body dynamic [1], [8].
{"title":"Quantized Kepler-Coulomb dynamical models on two-dimensional constant curvature spaces","authors":"Agnieszka Martens","doi":"arxiv-2409.09776","DOIUrl":"https://doi.org/arxiv-2409.09776","url":null,"abstract":"The paper is continuation of [6] where we have discussed some classical and\u0000quantization problems of rigid bodies of infinitesimal size moving in\u0000Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical\u0000models on sphere and pseudosphere. Here we concentrate on Kepler-Coulomb\u0000potential models. We have used formulated in [6] the two-dimensional situation\u0000on the quantum level. The Sommerfeld polynomial method is used to perform the\u0000quantization of such problems. The quantization of two-dimensional problems may\u0000have something to do with the dynamics of graphens, fullerens and nanotubes.\u0000This problem is also nearly related to the so-called restricted problems of\u0000rigid body dynamic [1], [8].","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Settino, L. Salatino, L. Mariani, M. Channab, L. Bozzolo, S. Vallisa, P. Barillà, A. Policicchio, N. Lo Gullo, A. Giordano, C. Mastroianni, F. Plastina
Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.
{"title":"Memory-Augmented Quantum Reservoir Computing","authors":"J. Settino, L. Salatino, L. Mariani, M. Channab, L. Bozzolo, S. Vallisa, P. Barillà, A. Policicchio, N. Lo Gullo, A. Giordano, C. Mastroianni, F. Plastina","doi":"arxiv-2409.09886","DOIUrl":"https://doi.org/arxiv-2409.09886","url":null,"abstract":"Reservoir computing (RC) is an effective method for predicting chaotic\u0000systems by using a high-dimensional dynamic reservoir with fixed internal\u0000weights, while keeping the learning phase linear, which simplifies training and\u0000reduces computational complexity compared to fully trained recurrent neural\u0000networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth\u0000of Hilbert spaces in quantum systems, allowing for greater information\u0000processing, memory capacity, and computational power. However, the original QRC\u0000proposal requires coherent injection of inputs multiple times, complicating\u0000practical implementation. We present a hybrid quantum-classical approach that\u0000implements memory through classical post-processing of quantum measurements.\u0000This approach avoids the need for multiple coherent input injections and is\u0000evaluated on benchmark tasks, including the chaotic Mackey-Glass time series\u0000prediction. We tested our model on two physical platforms: a fully connected\u0000Ising model and a Rydberg atom array. The optimized model demonstrates\u0000promising predictive capabilities, achieving a higher number of steps compared\u0000to previously reported approaches.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we would like to point out the possibility of generating a class of exactly solvable convection-diffusion-reaction equation in similarity form with intrinsic supersymmetry, i.e., the solution and the diffusion coefficient of the equation are supersymmetrically related through their similarity scaling forms.
{"title":"A class of exactly solvable Convection-Diffusion-Reaction equations in similarity form with intrinsic supersymmetry","authors":"Choon-Lin Ho","doi":"arxiv-2409.09503","DOIUrl":"https://doi.org/arxiv-2409.09503","url":null,"abstract":"In this work we would like to point out the possibility of generating a class\u0000of exactly solvable convection-diffusion-reaction equation in similarity form\u0000with intrinsic supersymmetry, i.e., the solution and the diffusion coefficient\u0000of the equation are supersymmetrically related through their similarity scaling\u0000forms.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To demonstrate the implication of the recent important theorem by Roos, Teufel, Tumulka, and Vogel [1] in a simple but nontrivial example, we study thermalization in the two-dimensional Ising model in the low-temperature phase. We consider the Hamiltonian $hat{H}_L$ of the standard ferromagnetic Ising model with the plus boundary conditions and perturb it with a small self-adjoint operator $lambdahat{V}$ drawn randomly from the space of self-adjoint operators on the whole Hilbert space. Suppose that the system is initially in a classical spin configuration with a specified energy that may be very far from thermal equilibrium. It is proved that, for most choices of the random perturbation, the unitary time evolution $e^{-i(hat{H}_L+lambdahat{V})t}$ brings the initial state into thermal equilibrium after a sufficiently long and typical time $t$, in the sense that the measurement result of the magnetization density at time $t$ almost certainly coincides with the spontaneous magnetization expected in the corresponding equilibrium.
{"title":"Macroscopic thermalization by unitary time-evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Teufel-Tumulka-Vogel theorem","authors":"Hal Tasaki","doi":"arxiv-2409.09395","DOIUrl":"https://doi.org/arxiv-2409.09395","url":null,"abstract":"To demonstrate the implication of the recent important theorem by Roos,\u0000Teufel, Tumulka, and Vogel [1] in a simple but nontrivial example, we study\u0000thermalization in the two-dimensional Ising model in the low-temperature phase.\u0000We consider the Hamiltonian $hat{H}_L$ of the standard ferromagnetic Ising\u0000model with the plus boundary conditions and perturb it with a small\u0000self-adjoint operator $lambdahat{V}$ drawn randomly from the space of\u0000self-adjoint operators on the whole Hilbert space. Suppose that the system is\u0000initially in a classical spin configuration with a specified energy that may be\u0000very far from thermal equilibrium. It is proved that, for most choices of the\u0000random perturbation, the unitary time evolution\u0000$e^{-i(hat{H}_L+lambdahat{V})t}$ brings the initial state into thermal\u0000equilibrium after a sufficiently long and typical time $t$, in the sense that\u0000the measurement result of the magnetization density at time $t$ almost\u0000certainly coincides with the spontaneous magnetization expected in the\u0000corresponding equilibrium.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"5 2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively handle multiparameter inputs. Experiments demonstrate that our methodology not only accelerates computations but also significantly enhances generalization performance, even with varying scattering properties and noisy data. The robustness and adaptability of our framework provide crucial insights and methodologies, extending its applicability to a broad spectrum of scattering problems. These advancements mark a significant step forward in the field, offering a scalable solution to traditionally complex inverse problems.
{"title":"Neumann Series-based Neural Operator for Solving Inverse Medium Problem","authors":"Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi","doi":"arxiv-2409.09480","DOIUrl":"https://doi.org/arxiv-2409.09480","url":null,"abstract":"The inverse medium problem, inherently ill-posed and nonlinear, presents\u0000significant computational challenges. This study introduces a novel approach by\u0000integrating a Neumann series structure within a neural network framework to\u0000effectively handle multiparameter inputs. Experiments demonstrate that our\u0000methodology not only accelerates computations but also significantly enhances\u0000generalization performance, even with varying scattering properties and noisy\u0000data. The robustness and adaptability of our framework provide crucial insights\u0000and methodologies, extending its applicability to a broad spectrum of\u0000scattering problems. These advancements mark a significant step forward in the\u0000field, offering a scalable solution to traditionally complex inverse problems.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of POVM decompositions. The latter arise from integrals over families of bounded positive operators. Crucially, these operators have the same locality properties as the underlying field operators. We use the decompositions to construct families of quantum operations implementing measurements of the field observables. Again, the quantum operations have the same locality properties as the field operators. What is more, we show that these quantum operations do not lead to superluminal signaling and are possible measurements on quantum fields in the sense of Sorkin.
{"title":"Spectral decomposition of field operators and causal measurement in quantum field theory","authors":"Robert OecklCCM-UNAM","doi":"arxiv-2409.08748","DOIUrl":"https://doi.org/arxiv-2409.08748","url":null,"abstract":"We construct the spectral decomposition of field operators in bosonic quantum\u0000field theory as a limit of a strongly continuous family of POVM decompositions.\u0000The latter arise from integrals over families of bounded positive operators.\u0000Crucially, these operators have the same locality properties as the underlying\u0000field operators. We use the decompositions to construct families of quantum\u0000operations implementing measurements of the field observables. Again, the\u0000quantum operations have the same locality properties as the field operators.\u0000What is more, we show that these quantum operations do not lead to superluminal\u0000signaling and are possible measurements on quantum fields in the sense of\u0000Sorkin.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：